Question Number 77991 by peter frank last updated on 12/Jan/20 $${If}\:\:{P}_{\mathrm{1}} \:\:{P}_{\mathrm{2}} \:\:{P}_{\mathrm{3}} \:\:{will}\:{be}\:{taken} \\ $$$${as}\:{point}\:{in}\:{an}\:{Argand} \\ $$$${diagram}\:{representing} \\ $$$${complex}\:{number} \\ $$$${Z}_{\mathrm{1}} ,{Z}_{\mathrm{2}} ,{Z}_{\mathrm{3}} \:\:{and}\:{point}…
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Question Number 142729 by mohammad17 last updated on 04/Jun/21 $${prove}:\frac{{d}}{{dz}}\left({tan}^{−\mathrm{1}} {z}\right)=\frac{\mathrm{1}}{\mathrm{1}+{z}^{\mathrm{2}} }\:{in}\:{complex}\:{number} \\ $$$${help}\:{me}\:{sir} \\ $$$$ \\ $$ Answered by mathmax by abdo last updated…
Question Number 141681 by ZiYangLee last updated on 22/May/21 $$\mathrm{On}\:\mathrm{the}\:\mathrm{Argand}\:\mathrm{Diagram},\:\mathrm{the}\:\mathrm{variable}\:\mathrm{point} \\ $$$$\mathrm{Z}\:\mathrm{represents}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:{z}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point} \\ $$$$\mathrm{Z}\:\mathrm{which}\:\mathrm{moves}\:\mathrm{such}\:\mathrm{that}\:\mid\frac{{z}−\mathrm{1}}{{z}+\mathrm{2}}\mid=\mathrm{2} \\ $$ Answered by MJS_new last updated on 22/May/21…
Question Number 75742 by Gazella thomsonii last updated on 16/Dec/19 $$\mathrm{plz}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{my}\:\mathrm{handsome}\:\mathrm{guys}\:\mathrm{and}\:\mathrm{sisters}… \\ $$$$\mathrm{complex}\:\mathrm{integral}\:\int_{−\infty} ^{+\infty} \:\frac{{e}^{\boldsymbol{{i}}{t}} }{\:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\mathrm{d}{t} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 75741 by Gazella thomsonii last updated on 16/Dec/19 $$\mathrm{solve}\:\mathrm{complex}\:\mathrm{integral} \\ $$$$\int_{−\infty} ^{+\infty} \:\frac{{e}^{\boldsymbol{{i}}{t}} }{\:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\mathrm{d}{t}=???? \\ $$$$\mathrm{plz}…….\mathrm{help}\:\mathrm{me}…\mathrm{T}\frown\mathrm{T}\:\:\: \\ $$$$\mathrm{my}\:\mathrm{handsome}\:\mathrm{brothers}\:\mathrm{and}\:\mathrm{sisters}… \\ $$ Terms of…
Question Number 75721 by Gazella thomsonii last updated on 15/Dec/19 $$\mathrm{solve}\:\mathrm{this}\:\mathrm{complex}\:\mathrm{integral}\int_{−\infty} ^{+\infty} \:\frac{{e}^{\boldsymbol{{i}}{t}} }{\:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}\mathrm{d}{t} \\ $$ Commented by MJS last updated on 15/Dec/19 $$\underset{−\infty}…
Question Number 75509 by ~blr237~ last updated on 12/Dec/19 $$\mathrm{Give}\:\mathrm{the}\:\mathrm{exponentional}\:\mathrm{form}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{complex}\:\mathrm{Z}=\frac{\mathrm{1}−\mathrm{cos}\theta+\mathrm{itan}\theta}{\mathrm{1}+\mathrm{cos}\theta−\mathrm{isin}\theta} \\ $$ Answered by MJS last updated on 12/Dec/19 $$\frac{\mathrm{1}−{c}+\mathrm{i}{t}}{\mathrm{1}+{c}−\mathrm{i}{s}}=\frac{{c}^{\mathrm{2}} −\mathrm{2}{c}−{st}+\mathrm{1}}{{c}^{\mathrm{2}} −\mathrm{2}{c}+{s}^{\mathrm{2}} +\mathrm{1}}−\frac{{cs}+{ct}−{s}−{t}}{{c}^{\mathrm{2}}…
Question Number 75306 by 21042004 last updated on 09/Dec/19 $${Use}\:{Venn}\:{diagram}\:{to} \\ $$$${represent}\:{the}\:{set}\:{of}\:{natural} \\ $$$${numbers},\:{integers},\:{rational} \\ $$$${numbers},\:{irrational} \\ $$$${numbers},\:{real}\:{numbers}, \\ $$$${complex}\:{numbers} \\ $$ Commented by mr…
Question Number 140784 by ajfour last updated on 12/May/21 $${Let}\:{the}\:{i}-{j}\:{plane}\:{be}\:{the}\:{complex} \\ $$$$\:{plane},\:{with}\:{basic}\:{operations} \\ $$$$\:\:{ij}=−{i} \\ $$$$\:\:{ji}=−{j} \\ $$$$\:\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\:\:{j}^{\mathrm{2}} =−\mathrm{1} \\ $$$${z}={r}+{xi}+{yj}\:\:\:\:{w}={s}+{pi}+{qj} \\…
Question Number 9661 by geovane10math last updated on 23/Dec/16 $$\left.{a}\right)\:\mathrm{2}^{{i}} \:=\: \\ $$$$ \\ $$$$\left.{b}\right)\:\left({a}_{\mathrm{1}} \:+\:{b}_{\mathrm{1}} {i}\right)^{{a}_{\mathrm{2}} \:+\:{b}_{\mathrm{2}} {i}} \:=\: \\ $$$${Powers}\:{of}\:{complex}\:{numbers}\:??? \\ $$ Commented…